I like Sai Kung and think you would find it fine. However, the word "village" has different meanings to different people and I do not see "villages" when I walk through Sai Kung (as I do quite frequently). I see urban sprawl with very ugly houses and often weird configurations. So don't be surprised if you find it less appealing and more ugly when you get here - it's better than most of HK! Your budget seems plenty to find a house.
Other options where there is a sense of community - the other obvious one that springs to mind is Discovery Bay. Not sure what the commute time from there is to TST - probably the best bet is actually two ferry's, bizarre as that might sound! But there is a strong community of expat mothers over there.
Gold COast also has an expat community - very diverse nationalities and lots with young children. Here you would get a beach house (well, technically one floor of a beach house) with your budget. 30 min commute to TST on the resident bus in the mornings (only two departure times though, but there are other options).
The best advice is to come and see. Go and spend some time in Sai Kung and suss it out. Travel around, walk around, talk to many agents, get a feel for the place. Even there one village will the different from another. Take every agents website with a pinch of salt - they all lie and doctor photos - get a serviced appt for a couple of weeks when you arrive and travel around.
Good luck. It's a great place to come - not without issues as you will find, but a really exciting expat destination with a good community to join.